I have no idea if it works, because I've got a beard
But I know a link who does.
To all you faux-scientists cheerfully labelling people as nutters etc. Here's your chance to use actual scientific method.
https://pyramidrazorsharpener.wordpress.com/
Give it a go for a couple weeks and let us know how you got on. If you tried it and it's crap then you can start the badmouthing. Yes I know actually doing research is loads more trouble than just spouting off sorry for the inconvenience.
In my dim distant memory I think I remember some bloke who allegedly got this working in the old Soviet Union when new razor blades were rare to nonexistent.